I don't use pin backs (although you could), I prefer clips. Here's what you will need:
Silk or fabric flowers (you can buy them singly or in a bunch at craft stores)
Clips There are a variety of clips available in the jewelry finding department of craft stores. They are very inexpensive.
Hot glue gun
Exacto or craft knife, scissors
Pull the bloom from the stem. There is a plastic-y connector. The keep the flower from coming apart, I use the hot tip of the glue gun to melt the plastic down flat.
Squeeze hot glue across the back of the flower in an area slightly smaller than the felt. The TOP of the clip will be AGAINST the petals. Open the clip and lay the felt across then press onto the hot glue (caution ... HOT!) When the glue cools, the clip will stay in place.
To fancy it up even more, cut away the bulk of the plastic middle and hot glue in a button, bead or jewel.